Predicting Multivariate Response in Linear Regression Model

Srivastava, M. S.; Solanky, Tumulesh K. S.

doi:10.1081/sac-120017497

Cited by 13 publications

(17 citation statements)

References 14 publications

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“…In the case of Chemometrics data, the L p -SVS estimates perform identically and they are the most precise. Their CVE value of 0.18 is slightly smaller than the values reported by Lutz and Bühlmann (2006) and clearly smaller than those by Breiman and Friedman (1997) and Srivastava and Solanky (2003). Shrinking without selection seems to work well for Chemometrics data.…”

Section: Experiments On Real Datacontrasting

confidence: 38%

“…Either a separate model is built for each response variable, or a single model is used to estimate all the responses simultaneously. Breiman and Friedman (1997) and Srivastava and Solanky (2003) present simultaneous estimation techniques that have advantages over the separate model building, especially when the responses are correlated. Correlation among the responses is typical in many applications, for instance, in the field of chemometrics (Burnham et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

“…Highly correlated inputs cause the problem of collinearity: model interpretation is misleading as the importance of an input in the model can be compensated by another input. Traditional methods for meeting these problems are pure input selection (Sparks et al, 1985), regularization or shrinking (Breiman and Friedman, 1997;Srivastava and Solanky, 2003), and subspace methods (Abraham and Merola, 2005). Shrinking means that the regression coefficients are constrained such that the unimportant inputs tend to have coefficient values close to zero.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Input selection and shrinkage in multiresponse linear regression

Similä¹,

Tikka²

2007

Computational Statistics & Data Analysis

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The regression problem of modeling several response variables using the same set of input variables is considered. The model is linearly parameterized and the parameters are estimated by minimizing the error sum of squares subject to a sparsity constraint. The constraint has the effect of eliminating useless inputs and constraining the parameters of the remaining inputs in the model. Two algorithms for solving the resulting convex cone programming problem are proposed. The first algorithm gives a pointwise solution, while the second one computes the entire path of solutions as a function of the constraint parameter. Based on experiments with real data sets, the proposed method has a similar performance to existing methods. In simulation experiments, the proposed method is competitive both in terms of prediction accuracy and correctness of input selection. The advantages become more apparent when many correlated inputs are available for model construction.

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Section: Experiments On Real Datacontrasting

confidence: 38%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Input selection and shrinkage in multiresponse linear regression

Similä¹,

Tikka²

2007

Computational Statistics & Data Analysis

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“…MARS has been used with other materials (Srivastava and Solanky, 2003;Put et al, 2004) and was reported to give better results as compared to other linear and nonparametric regression techniques like generalized linear models, artificial neutral networks, and classification and regression trees.…”

Section: Discussionmentioning

confidence: 99%

Modeling temporal variability of soil CO2 emissions from an apple orchard in the Harran Plain of southeastern Turkey

Bilgili¹,

Yilmaz²,

İkinci³

2013

Turk J Agric For

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IntroductionIncreased emission of greenhouse gases such as CO 2 , methane (CH 4 ), and nitrous oxide (N 2 O) to the atmosphere is closely associated with land use change, the use of fossil fuels, forest fires, emissions from automobiles, agricultural production, and other anthropogenic activities (Sauerbeck, 2001). The CO 2 concentration of the atmosphere has changed significantly since the Industrial Revolution, increasing from 280 ppm to 390 ppm (August 2011 Mauna Loa Station, NOAA; http://co2now.org/ Current-CO2/CO2-Now/noaa-mauna-loa-co2-data. html), and it may double by the end of the 21st century if greenhouse gases continue being emitted (Lal, 2003). Soils contribute about 20% of the total CO 2 released to the atmosphere (Sauerbeck, 2001). Better management of soil organic carbon can reduce greenhouse gas emissions and increase soil fertility (Sauerbeck, 2001).Monitoring CO 2 fluxes from soils can reveal important information about microbial activity, plant root respiration, soil-atmosphere interactions, soil energy and carbon budgets, and plant production, allowing us to better understand trends and find ways to mitigate emissions (Lal, 2003). The amounts of CO 2 released from the soil to the atmosphere varies greatly based on different land use types, agricultural activities, soil characteristics, and climate (Smith et al., 2000), and it generally ranges from 0.1 to 6 g CO 2 m -2 h -1 for agricultural soils (Sauerbeck 2001). Extensive research documents how temporal and spatial variations in CO 2 emissions are controlled by soil temperature (Almaraz et al., 2009), soil water content (La Scala et al., 2006), soil organic matter content and substrate quality (Frank et al., 2006), and interaction between significant properties (Pangle and Seiler, 2002). These variables impact the activity of roots and

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“…Multiresponse models have advantages over separate models when the responses are correlated [11], [12]. Common subset selection of inputs can be motivated by the computational burden of repeating input selection for each response variable separately [13].…”

Section: Introductionmentioning

confidence: 99%

Common Subset Selection of Inputs in Multiresponse Regression

Similä¹,

Tikka²

The 2006 IEEE International Joint Conference on Neural Network Proceedings

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Abstract-We propose the Multiresponse Sparse Regression algorithm, an input selection method for the purpose of estimating several response variables. It is a forward selection procedure for linearly parameterized models, which updates with carefully chosen step lengths. The step length rule extends the correlation criterion of the Least Angle Regression algorithm for many responses. We present a general concept and explicit formulas for three different variants of the algorithm. Based on experiments with simulated data, the proposed method competes favorably with other methods when many correlated inputs are available for model construction. We also study the performance with several real data sets.

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Predicting Multivariate Response in Linear Regression Model

Cited by 13 publications

References 14 publications

Input selection and shrinkage in multiresponse linear regression

Input selection and shrinkage in multiresponse linear regression

Modeling temporal variability of soil CO2 emissions from an apple orchard in the Harran Plain of southeastern Turkey

Common Subset Selection of Inputs in Multiresponse Regression

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